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Advanced Quantum Technologies

Work Statistics and Entanglement Across the Fermionic Superfluid‐Insulator Transition

Krissia Zawadzki, G. A. Canella, V. V. França, Irene D’Amico

Published Jan 20, 2024• 5 citations
Publisher

Abstract

Abstract Entanglement in many‐body systems may display quantum phase transition signatures, and analogous insights are emerging in the study of work fluctuations. Here, the fermionic superfluid‐to‐insulator transition (SIT) is considered and related to its entanglement properties and its work distribution statistics. Using the attractive fermionic Hubbard model with randomly distributed impurities, the work distribution is analyzed under two quench protocols triggering the SIT. In the first, the concentration of impurities is increased; in the second, the impurities' disorder strength is varied. The results indicate that, at criticality, the entanglement is minimized while the average work is maximized. This study demonstrates that, for this state, density fluctuations vanish at all orders, resulting in all central moments of the work probability distribution being precisely zero. For systems undergoing a precursor to the transition (short chains with finite impurity potential) numerical results confirm these predictions, with higher moments further from the ideal results. For both protocols, at criticality, the system absorbs the most energy with almost no penalty in terms of fluctuations: ultimately this feature can be used to implement a quantum critical battery. The impact of temperature on this critical behaviour is also investigated and shown to favor work extraction for high enough temperatures.

DOI
10.1002/qute.202300237

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Abstract Entanglement in many‐body systems may display quantum phase transition signatures, and analogous insights are emerging in the study of work fluctuations. Here, the fermionic superfluid‐to‐insulator transition (SIT) is considered and related to its entanglement properties and its work distribution statistics. Using the attractive fermionic Hubbard model with randomly distributed impurities, the work distribution is analyzed under two quench protocols triggering the SIT. In the first, the concentration of impurities is increased; in the second, the impurities' disorder strength is varied. The results indicate that, at criticality, the entanglement is minimized while the average work is maximized. This study demonstrates that, for this state, density fluctuations vanish at all orders, resulting in all central moments of the work probability distribution being precisely zero. For systems undergoing a precursor to the transition (short chains with finite impurity potential) numerical results confirm these predictions, with higher moments further from the ideal results. For both protocols, at criticality, the system absorbs the most energy with almost no penalty in terms of fluctuations: ultimately this feature can be used to implement a quantum critical battery. The impact of temperature on this critical behaviour is also investigated and shown to favor work extraction for high enough temperatures.
Entanglement in many-body systems may display interesting signatures of quantum phase transitions and similar properties are starting to be encountered in the analysis of work fluctuations. Here, we consider the fermionic superfluid-to-insulator transition (SIT) and relate its entanglement properties with its work distribution statistics. The SIT is modeled by the attractive fermionic Hubbard model in the presence of randomly distributed impurities. The work distribution is calculated across two quench protocols, both triggering the SIT. In the first, the concentration of impurities is increased; in the second, the impurities' disorder strength is varied. Our results indicate that, the critical state that induces minimization of the entanglement also maximizes the average work. We demonstrate that, for this state, density fluctuations vanish at all orders, hence all central moments of the work probability distribution are exactly zero at criticality. For systems undergoing a precursor to the transition (short chains with finite impurity potential) numerical results confirm these predictions, with higher moments further from the ideal result. For both protocols, at criticality, the system absorbs the most energy with almost no penalty in terms of fluctuations: ultimately this feature could be used to implement a quantum critical battery. The effects of temperature on these signatures of critical behaviour are also investigated and shown to favor work extraction for high enough temperatures.
Abstract We use entanglement to track the superfluid-insulator transition (SIT) in disordered fermionic superfluids described by the one-dimensional Hubbard model. Entanglement is found to have remarkable signatures of the SIT driven by i) the disorder strength V, ii) the concentration of impurities C and iii) the particle density n. Our results reveal the absence of a critical potential intensity on the SIT driven by V, i.e. any small V suffices to decrease considerably the degree of entanglement: it drops ∼50% for V = −0.25t. We also find that entanglement is non-monotonic with the concentration C, approaching to zero for a certain critical value CC. This critical concentration is found to be related to a special type of localization, here named as fully-localized state, which can be also reached for a particular density nC. Our results show that the SIT driven by n or C has distinct nature whether it leads to the full localization or to the ordinary one: it is a first-order quantum phase transition only when leading to full localization. In contrast, the SIT driven by V is never a first-order quantum phase transition independently on the type of localization reached.
We investigate the disorder-driven superconductor to insulator quantum phase transition (SIT) in an interacting fermion model using determinantal quantum Monte Carlo (QMC) methods. The disordered superconductor is modeled by an attractive Hubbard model with site disorder chosen randomly from a uniform distribution. The superconducting state which exists for small disorder is shown to evolve into an insulating phase beyond a critical disorder. The transition is tracked by the vanishing of (a) the superfluid stiffness, and (b) the charge stiffness or the delta function peak in the optical conductivity at zero frequency. We also show the behavior of the charge, spin, pair, and current correlations in the presence of disorder. Results for the temperature dependence of the dc conductivity, obtained by an approximate analytic continuation technique, are also presented both in the metallic phase above Tc{T}_{c}Tc​ and the insulating phase. We discuss some of the complications in extracting the resistance at the transition point.
The thermodynamic behavior of out-of-equilibrium quantum systems in finite-time dynamics encompasses the description of energy fluctuations, which dictates a series of the system's physical properties. In addition, strong interactions in many-body systems strikingly affect the energy-fluctuation statistics along a nonequilibrium dynamics. By driving transient currents to oppose the precursor to the metal-Mott-insulator transition in a diversity of dynamical regimes, we show how increasing many-body interactions dramatically affect the statistics of energy fluctuations and, consequently, the extractable work distribution of finite Hubbard chains. Statistical properties of such distributions as its skewness with its impressive change across the transition can be related to irreversibility and entropy production. Even for slow driving rates, the quasi quantum phase transition hinders equilibration, increasing the process irreversibility, and inducing strong features in the work distribution. In the Mott-insulating phase, the work fluctuation-dissipation balance gets modified with the irreversible entropy production dominating over work fluctuations. Because of this, effects of an interaction-driven quantum phase transition on thermodynamic quantities and irreversibility must be considered in the design of protocols in small-scale devices for application in quantum technology. Eventually, such many-body effects can also be employed in work extraction and refrigeration protocols on a quantum scale.
It is well known that bosons on an optical lattice undergo a second-order superfluid-insulator transition (SIT) when the lattice potential increases. In this paper, we study SIT when fermions coexist with the bosons. We find that the critical properties of particle-hole symmetric SIT with dynamical exponent z=1z=1z=1 is modified when fermions are present; it either becomes a fluctuation-driven first-order transition or a different second-order transition. On the other hand, the more generic particle-hole asymmetric (with z=2z=2z=2) SIT is stable against coupling with fermions. We also discuss pairing interaction between fermions mediated by quantum critical fluctuations near SIT and show that the fermion pairing and/or superfluid transition temperature peaks near SIT when a single species of fermion is present.